Question

side of a triangle is in ratio of 12:17:25 and it perimeter is 540cm. find it area​

Answer 1

Given:

• Sides of triangle are in ratio of 12:17:25.

• Perimeter = 540 cm

To calculate:

• Area of the triangle.

Calculation:

Let's calculate the measure of sides first.

Let,

Side of the triangle :

• a = 12x cm
• b = 17x cm
• c = 25x cm

As we know that,

→ Perimeter of the triangle = Sum of all sides

→ Perimeter of the triangle = a + b + c

According to the question,

→ 540 cm = 12x cm + 17x cm + 25x cm

→ 540 = 12x + 17x + 25x

→ 540 = 54x

→ $\sf {\cancel {\dfrac{540}{54}} }$ = x

→ 10 = x

So, the sides of the triangle are :

• a = 12x

→ a = (12 × 10) cm

→ a = 120 cm

• b = 17x

→ b = (17 × 10) cm

→ b = 170 cm

• c = 25x

→ c = (25 × 10) cm

→ c = 25 cm

Now, let's calculate area of the ∆ :

By using heron's formula :

→ Area of the ∆ = √[s(s-a)(s-b)(s-c)]

⠀⠀⠀⠀⠀⠀→ s = semi perimeter

⠀⠀⠀⠀⠀⠀→ s = $\sf { \dfrac{Perimeter}{2} }$

⠀⠀⠀⠀⠀⠀→ s = $\sf { \dfrac{540}{2} cm }$

⠀⠀⠀⠀⠀⠀→ s = 270 cm

→ Area of the ∆ = √[270(270-120)(270-170)(270-250)] cm²

→ Area of the ∆ = √(270 × 150 × 100 × 20) cm²

→ Area of the ∆ = √(81000000) cm²

→ Area of the ∆ = √(81 × 100 × 100 × 100) cm²

→ Area of the ∆ = 9 × 10 × 10 × 10 cm²

→ Area of the ∆ = 9000 cm²

Therefore, the area of the triangle is 9000 cm².